Closed form solutions to a generalization of the Solow growth model

Abstract:
The Solow growth model assumes that labor force grows exponentially. This is not a realistic assumption because, exponential growth implies that population increases to infinity as time tends to infinity. In this paper we propose replacing the exponential population growth with a simple and more realistic equation - the Von Bertalanffy model. This model utilizes three hypotheses about human population growth: (1) when population size is small, growth is exponential; (2) population is bounded; and (3) the rate of population growth decreases to zero as time tends toward infinity. After making this substitution, the generalized Solow model is then solved in closed form, demonstrating that the intrinsic rate of population growth does not influence the long-run equilibrium level of capital per worker. We also study the revised model's stability, comparing it with that of the classical model.